People have been giving gifts to celebrate various anniversaries for centuries. The earliest recorded instances of giving gifts at wedding anniversaries come from Central Europe, and there is a tradition of using a different material to celebrate each milestone in a couple's life e.g a gift with a wooden theme after 5 years of marriage, and an increasingly expensive material used as the years go by.
"The practice of observing the wedding anniversary, while primarily an excuse for gift-giving, probably has underlying it a belief in the correspondence of certain luck-bringing substances with a distinct number of years." Source: Funk & Wagnalls Standard Dictionary of Folklore, Mythology, and Legend
In Germany in the mid ages it was customary for a wife to receive silver garlands after 25 years and in gold after 50 years which gave rise to the "silver wedding" and "golden wedding" tradition. It was probably after Queen Victoria celebrated her sixtieth year on the throne, called the 'Diamond Jubilee' that diamonds came to be associated with 60 years. They are also associated with 75 years.
The earliest reference of giving a present in wood after 5 years come in the late 19th century, but in Wales Wooden Love Spoons have been given to celebrate all anniversaries, especially among the general population.
Of course the giver does not have to adhere strictly to the materials traditionally associated with the different stages, and there are many interesting ways of giving a gift which suggests the number of years a couple have been married other than a gift in the actual material associated with the number of years.
"The passing of another year together marks a deepening of the couple's commitment, an accumulation of time irreplaceable. To help in celebrating these occasions are special gifts, one assigned to each anniversary and each with its own material and symbolic value. In the United States, the wedding anniversary symbols begin simply, with paper and flowers, and gradually increase in substance and value. The order of gifts reflects the investment that the couple gives of themselves to each other. In Germany, by comparison, couples use a list of symbols that represent the progressive strengthening of the marriage relationship." Source: Gretchen Scoble and Ann Field, The Meaning of Wedding Anniversaries, page 7.